The desired impedance dynamics can be achieved for a robot if and only if an impedance error converges to zero or a small neighborhood of zero. Although the convergence of impedance errors is important, it is seldom obtained in the existing impedance controllers due to robots modeling uncertainties and external disturbances. This brief proposes two composite learning impedance controllers (CLICs) for robots with parameter uncertainties based on whether a factorization assumption is satisfied or not. In the proposed control designs, the convergence of impedance errors, reflected by the convergence of parameter estimation errors and some auxiliary errors, is achieved by using composite learning laws under a relaxed excitation condition. The theoretical results are proven based on the Lyapunov theory. The effectiveness and advantages of the proposed CLICs are validated by simulations on a parallel robot in three cases.